This is an odd business for most physicists and engineers, who are used to caring about details! A graded index fiber optic cable, for instance, must be made with precision, confining light rays with a particular spatial distribution of refractive index to minimize dispersion. Here we have a completely different kind of theory, where the design process doesn't even mention the details of the region where the mode is to be confined. This peculiar insensitivity to the form of the interface (often called `topological protection') was perhaps first appreciated by Volkov and co–workers, who were concerned with the physics of electrons around electronic contacts [1]}, [2]}. The significance of topology was appreciated later [3]}, [4]}, in connection with earlier work on the quantum hall effect [5]}, [6]}.
